The DirectX 11 Compute Shader, also known as Direct Compute, is a powerful but complex feature. In addition to the Windows DirectX Graphics documentation, here is a list of resources for learning to use this technology:

Gamefest 2008 - Direct3D 11 Compute Shader —More Generality for Advanced Techniques
MS Downloads

Game Developer Conference 2009 - Direct3D11 Multithreaded Rendering and Compute
MS Downloads

Gamefest 2010 - DirectX 11 DirectCompute – A Teraflop for Everyone
MS Downloads

Channel 9 DirectCompute Lecture Series
Channel 9

PDC 2009 - DirectCompute Hands On Lab
MSDN Code Gallery

The following samples:
BasicCompute11, ComputeShaderSort11, BC6HBC7EncoderDecoder11AdaptiveTessellationCS40, FluidCS11, HDRToneMappingCS11, NBodyGravityCS11, and OIT11

NVIDIA and AMD also did a number of presentations at Game Developers Conference, including the following talks covering DirectCompute:

GDC 2010 - DirectCompute Performance on DX11 Hardware
NVIDIA Developer Website | AMD Developer Website

GDC 2009 - Shader Model 5.0 and Compute Shader (AMD)
AMD Developer Website

GDC 2009 - DirectX 10/11Visual Effects (NVIDIA)
NVIDIA Developer Website

Intel has a whitepaper on using DirectCompute for their "Ivy Bridge" platform that supports Feature Level 11.0

http://software.intel.com/en-us/articles/microsoft-directcompute-on-intel-ivy-bridge-processor-graphics/

Related: Getting Started with Direct3D 11